RE: Variational Methods

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Godfrey Loudner" <ggreen@xxxxxxxx>

Hello Jared

The Maxwell equations are equivalent to the least action principles, so
we do need Maxwell either directly or indirectly. If one views the tesla
coil circuits as purely lumped with small damping, then all you say can
be done with differential equations. In fact it all can be found in
"Principles of Electricity, Page & Adams, Chapter XV" and done without
writing down a Lagrangian. Even I can redevelop the chapter XV content
in terms of Lagrangians. I suppose if I were teaching from Page & Adams,
I would assign the task as an exercise. Well I never assign any problem
I can't work myself. But the chapter XV content is an approximation
because the currents are assumed to be uniform. The currents in a tesla
coil secondary are not uniform. I was suggesting that in order to get a
more accurate picture of the secondary, perhaps least action principles
could be used. I think finding the associated Green's functions would be
a monumental task. Even if reasonable Green's functions could be found,
then one would probably have to resort to the voodoo techniques of
asymptotics, perturbation, or WKB approximations to make the process
give up interesting information. See "Advanced Mathematical Methods for
Scientists and Engineers I, Bender & Orszag".

Godfrey Loudner

-----Original Message-----
From: Tesla list [mailto:tesla@xxxxxxxxxx]
Sent: Friday, April 21, 2006 3:32 PM
To: tesla@xxxxxxxxxx
Subject: Variational Methods


Original poster: Jared E Dwarshuis <jdwarshui@xxxxxxxxx>

We dont need Green, Maxwell or Schwinger to solve this. We only need to
write our equations correctly and be - oh - so - carefull - in applying
the Lagrange. None of the steps are beyond the capability of someone who
has had linear and diff-eq

The setup gets messy, lots of places to drop the ball. So it is best to
have someone reality check your work as you go along.

Simple in the grand scheme of things but it would take me several days
of playing with examples in textbooks before I would feel confident
enough to begin hammering out equations.

Reminds me of the physics problems with multiple weights and pulleys.
God they are a pain. But they can be done by mere mortals with a lot of
patience.

My apology to Robert:

I used: La = T - V

Textbooks use: L = T - V

Didn't want to confuse inductance "L" with the Lagrange, which I labeled
"La" and yes.... T and V are energy.

Sincerely: Jared Dwarshuis